The (nonconservative) force propelling a 1.50 ×10^3-kg car up a mountain road does 4.70 ×10^6 J

step 1 of car is 1500 kg and it is given that the non -conservative force work done is 4 .70 into 10 to

The (nonconservative) force propelling a 1.50 ×10^3-kg car...

The (nonconservative) force propelling a $1.50 \times 10^{3}-\mathrm{kg}$ car up a mountain road does $4.70 \times 10^{6} \mathrm{J}$ of work on the car. The car starts from rest at sea level and has a speed of $27.0 \mathrm{m} / \mathrm{s}$ at an altitude of $2.00 \times 10^{2} \mathrm{m}$ above sea level. Obtain the work done on the car by the combined forces of friction and air resistance, both of which are nonconservative forces.

Key Concepts

Work-Energy Theorem

This principle states that the net work done on an object is equal to its change in kinetic energy. It is a fundamental tool for linking forces (such as those doing positive or negative work) with the motion of objects, by quantitatively relating energy input and energy transformations during motion.

Gravitational Potential Energy

Gravitational potential energy represents the energy an object possesses due to its position in a gravitational field. When an object is raised to a height, its potential energy increases by an amount given by the product of its mass, gravitational acceleration, and the change in height, reflecting the work needed to elevate the object against gravity.

Nonconservative Forces

Nonconservative forces, such as friction and air resistance, perform work that depends on the path taken, and they typically convert mechanical energy into other forms like heat. Unlike conservative forces, the energy lost to nonconservative forces cannot be recovered in a later process, thereby reducing the total mechanical energy of the system.

Energy Conservation

The law of energy conservation states that energy cannot be created or destroyed but only transformed from one form to another. In mechanical systems, this idea is used to account for how energy supplied by forces (both conservative and nonconservative) is partitioned between kinetic energy, potential energy, and energy dissipated due to factors such as friction.

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